Thanks! I'll quote it here for people searching:
No. Only one event card can be played with each new dinosaur. (But if you want to try something different and make it your own "house rule," feel free. Let us know how it works for you.)
To answer Diane's question, it worked too well. I was able to win as the "bone"r with the bonus prestige by only placing one dinosaur right at the end. Everything else was gained via attacks and other nefarious means.